logo

Expression of type ExprTuple

from the theory of proveit.physics.quantum.QPE

In [1]:
import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import ExprTuple, k, m
from proveit.linear_algebra import ScalarMult
from proveit.numbers import Exp, Mult, e, i, pi, two
from proveit.physics.quantum import NumBra, NumKet
from proveit.physics.quantum.QFT import InverseFourierTransform
from proveit.physics.quantum.QPE import _phase, _t
In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(NumBra(m, _t), InverseFourierTransform(_t), ScalarMult(Exp(e, Mult(two, pi, i, _phase, k)), NumKet(k, _t)))
expr:
In [3]:
# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")
Passed sanity check: expr matches stored_expr
In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
\left({_{t}}\langle m \rvert, {\mathrm {FT}}^{\dag}_{t}, \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \lvert k \rangle_{t}\right)
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
wrap_positionsposition(s) at which wrapping is to occur; 'n' is after the nth comma.()()('with_wrapping_at',)
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'leftleft('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0ExprTuple1, 2, 3
1Operationoperator: 4
operands: 5
2Operationoperator: 6
operand: 19
3Operationoperator: 8
operands: 9
4Literal
5ExprTuple10, 19
6Literal
7ExprTuple19
8Literal
9ExprTuple11, 12
10Variable
11Operationoperator: 13
operands: 14
12Operationoperator: 15
operands: 16
13Literal
14ExprTuple17, 18
15Literal
16ExprTuple26, 19
17Literal
18Operationoperator: 20
operands: 21
19Literal
20Literal
21ExprTuple22, 23, 24, 25, 26
22Literal
23Literal
24Literal
25Literal
26Variable